The circular drift-diffusion model (CDDM) is a stochastic sequential sampling model that describes choices and response times observed in tasks with a circular decision space (i.e., a bounded continuum; Smith, 2016).
Like many other accumulator models, the assumes that information gets accumulated over time, moving from a starting point located at the origin of a circle representing the decision space, towards its circumference. Responses made by participants are expressed in radians.
The CDDM considers four parameters.
The nondecision time \(\tau\)
The response criterion (i.e., the radius of the circle) \(\eta\).
A douplet of parameters related to the information provided by the stimulus: \(\mu_x\) and \(\mu_y\) OR \(\theta\) and \(\delta\).
Below we have a graphical representation of the CDDM (non-decision time is not included)
# 2: Define some parameter values and sample size ~ #
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #
# Some parameter values
par <- list("drift" = 1,
"theta" = pi,
"tzero" = 0.1,
"boundary" = 7)
n <- 5000 # No. samplesThe execution of this first algorithm took approximately 32.2845 seconds.
The execution of this second algorithm took approximately 32.2845 seconds.
par(pty="m")
par(mfrow=c(2,1),mar = c(3, 3, 3, 0))
# Choices
hist(X.RW$bivariate.data[,1], main="Choices on Random Walk",
xlim=c(0,2*pi), col="goldenrod4")
hist(X.MCMC[,1], main= "Choices on MCMC", xlim=c(0,2*pi), col="cyan4")